First we have to calculate the domains of #f(x)# and #g(x)#.
#f(x)# is defined for all real numbers - #D_f=RR#
#g(x)# is only defined when #2x-3>=0#
#2x>=3#
#x>=3/2#
#D_g=<3/2;+oo)#
The construction of product and quotient is just writing correct formulas using multiplication and division:
The product is #p(x)=(5x+7)*(sqrt(2x-3))#
The quotient is #q(x)=(5x-7)/sqrt(2x-3)#
The product is defined for those #x# where both factors are defined, so its domain is #D_p=<3/2;+oo)#
The domain of #q(x)# is smaller, because #g(x)# cannot be zero (it is in the denominator), so you have to exclude #3/2# from the domain.
Finally #D_q=(3/2;+oo)#
